Winning and losing in online gambling: Effects on within-session chasing

The tendency to continue or intensify gambling after losing (loss-chasing) is widely regarded as a defining feature of gambling disorder. However, loss-chasing in real gambling contexts is multifaceted, and some aspects are better understood than others. Gamblers may chase losses between multiple sessions or within a single session. Furthermore, within a session, loss-chasing can be expressed in the decision of (1) when to stop, (2) how much stake to bet, and (3) the speed of play after winning and losing. Using a large player-tracking data set (>2500 players, >10 million rounds) collected from the online commercial game Mystery Arena, we examined these three behavioral expressions of within-session loss-chasing. While the first two aspects (when to stop and how much stake to bet) have been examined previously, the current research is the first large-scale study to examine the effects of wins and losses on the speed of play in real gambling. The players were additionally assigned different involvement levels by the operator based on their gambling behavior on the operator’s own platform, which further allowed us to examine group differences in loss-chasing. We found that after winning, both the high- and low-involvement groups were less likely to stop, and increased the stake amount, thus showing win-chasing instead of loss-chasing in these two facets. After losing, both groups played more quickly though, which may reflect an urge to continue gambling (as an expression of loss-chasing). Wins and losses had a smaller influence on the speed of play for the high-involvement players, suggesting that they might have reduced sensitivity to wins and/or losses. Future work can further examine chasing in different gambling products and in people with gambling problems to assess the generalizability of these findings.


Classification of players by Gaming1
Gaming1 used several risk indicators to assign players into different risk levels (see Table S1) with an in-house machine learning model. The more risk triggers a player exhibits, the higher risk level a player receives. Note that some risk indicators used by Gaming1 overlap with the diagnostic criteria for gambling disorder in the DSM-5. For instance, the high frequency of play and the escalating deposit or bet amount (Gaming 1 criterion) may overlap with the need to gamble with increasing amounts of money to achieve the desired excitement (DSM-5 criterion); the use of multiple deposit methods (Gaming 1 criterion) may overlap with the reliance on others to provide money (to gamble; DSM-5 criterion); and lastly, the multiple canceled withdrawal or requests for cool-off periods (Gaming 1 criterion) may overlap with (unsuccessful) attempts to control or stop gambling . Although there are overlaps between the Gaming1 risk indicators and the DSM-5 diagnostic criteria, we acknowledge that the classification scheme by Gaming1 is not a validated measurement of problem gambling. It is therefore unclear whether the gamblers with higher risk levels indeed have greater problem gambling severity. For these reasons, we referred to the two groups as high-vs. low-involvement in the main text.

Table S1
Indicators used by Gaming1 to determine the risk level of a player.

Multiple Deposit Methods
• Several different deposit methods during the last 24 hours.
• Several days with multiple deposit methods in the last month.

Multiple Canceled Withdrawals
• Several canceled withdrawals during the last 24 hours.
• Several days with multiple canceled withdrawals in the last month.

Multiple Cool-off Periods
• Several cool-off requests within the last week, or last month.

High Frequency of Play
• High number of rounds within the week.

Deposit Amount Above Average
• The average deposit amount increased significantly in the short term.

Important Net Losses
• Important net loss in the last 24 hours or month or year.

Stake Amount Above Average
• The average stake amount of the 5 last playing days is significantly higher than the daily stake average. • Significant number of high daily stake average in the short term period.

Cumulative Net Gaming
• The cumulative net gaming crosses the lower limit of the band of normal play.

Age and gender distribution
Fig S1 shows the age by gender pyramids for both groups.

Figure S1
Age by gender pyramids for both groups. For the y axis, the age range (c, d] includes players who were older than c years old (i.e., >c) but not older than d years old (i.e., ≤ d).
The numbers next to the bars indicate the exact numbers of players in each age group.

Risk levels in the high-involvement group
As noted in the main text, the behavioral indicators of risk level (see Table S1) a player exhibits may vary over time. Accordingly, the risk level of a player can also vary.
This is the case for the high-involvement group in the current data (all players in the low-involvement group have consistently a risk level of 0). The Venn diagram below

Figure S2
Venn diagram showing the number of players in the high-involvement group with each risk level (determined by Gaming1) in the current data set. Number of Rounds

Figure S3
Histograms showing the numbers of players who played certain total numbers of sessions (top) and rounds (bottom). Note that the x axis is transformed. The height of a bar between a and b on the x axis denotes the number of players whose total session or round number is larger than a (> a) but not larger than b (<= b).

When to stop -without controlling for the overall stopping probabilities
Since the high-involvement players tended to have longer sessions, the overall probabilities to end a session was lower in the high-involvement group than in the low-involvement group. In the main text, we controlled for this overall stopping probability by dividing the probability of stopping after a win and after a loss by the overall stopping probability for each player (i.e., p(stop|loss)/p(stop − overall) and p(stop|win)/p(stop − overall), respectively). Here we present the results based on the raw stopping probabilities (i.e., p(stop|loss) and p(stop|win)) for completeness.

Figure S4
Probability of stopping after a win and after a loss. Error bars stand for 95% within-subject confidence intervals.
The ANOVA on stopping probabilities showed a significant main effect of involvement level, the previous outcome, and their interaction (Table S2). As can be seen in Figure S4, the high-involvement groups indeed had a lower probability to stop after both winning and losing, compared to the low-involvement group. Furthermore, in both groups, the probability to end a session was higher after a loss than after a win. Consistent with the results reported in the main text, both groups of players showed win-chasing, rather than loss-chasing.

Table S2
Statistical analyses on when to stop (no control for the overall stopping probabilities).

Group Player Round (Mean) Round (SD) Round (Min) Round (Max)
High To break down the interaction effect, we computed a difference score for each player (i.e., p(stop|loss) -p(stop|win)). A positive value indicates win-chasing in the facet of when to stop. The difference scores were then compared between the two groups. Contrary to the results in the main text (when the overall stopping probabilities were controlled for), with the raw stopping probabilities, the difference scores were descriptively smaller in the high-involvement group than in the low-involvement group. In other words, the tendency to chase wins seemed to be smaller in the high-involvement players. However, the effect size was rather small, and the Bayes factor was inconclusive (lnBF = -0.21, BF = 0.81).

When to stop -redefining 'sessions of play'
In the main text, we used the operator data to define one 'session of play'. That is, one session is from when a player logged into the platform till when they logged off. Each session received a unique session id in the operator data. However, players may take a break in their play without logging off, which would still be considered as one session in the data. Here, we report extra analyses in which we took such breaks in play (without logging off) into account when defining play sessions.
Players needed to make 13 consecutive responses in each game. If any of the 13 responses took longer than 10 minutes on a particular game, we assume that the player took a break and consider the corresponding game as the first round in a new 'session' of play. Such breaks in play occurred rather infrequently, in only about 0.050% of the games.
We nevertheless still examined whether the results on the decision of when to stop were influenced by this new definition of 'sessions of play'.

Figure S5
Histograms showing the numbers of players who played certain numbers of sessions (top) and the numbers of sessions that contained certain numbers of rounds (bottom; players from the same group were combined). Note the x axis is transformed. The height of a bar between a and b denotes the number of players (or the number of sessions / 100) whose session number (or round number) is larger than a (> a) but not larger than b (<= b). Next we compared the number of sessions, the mean and median number of rounds played in a session between the high-and the low-involvement group. The results can be found in Table S3. As would be expected, compared to the corresponding table in the main text, the average number of sessions played by players increased, while the average number of rounds per session (both the means and the medians) decreased, as the sessions in the original data have been divided into multiple shorter sessions. Importantly, the difference between the two groups remained: the high-involvement players overall played more sessions, and their play sessions also tended to be longer (i.e., containing more rounds).

Probability of stopping after a win and after a loss. Error bars stand for 95% within-subject confidence intervals.
We repeated the same analyses on the decision of when to stop, by controlling for the overall probability to end a session for each player. The overall pattern of the results remained the same ( Figure S6 and Table S4). Again, both groups of players were more likely to stop playing the game after a loss than after a win. Although the tendency to chase wins was descriptively larger in the high-risk group than in the low-risk group, the size of this effect was rather small, and the Bayes factor was inconclusive (lnBF = 0.39, BF = 1.48).

Table S4
Statistical analyses on when to stop (taking breaks longer than 10 minutes into account).

Change in stake levels
In the game, players could choose one out of ten stake amounts (0.25, 0.50, 1.00, 1.50, 2.00, 2.50, 5.00, 10.00, 15.00 and 20.00 euro, respectively). In the main text, we focused on the change in stake amount (euro cents) as a function of previous outcome.
Since the increment between two consecutive stake levels was not always the same, we additionally analyzed the change in stake levels. The ten stake amounts were first converted into stake levels, with 1 being the lowest stake of 0.25 euro and 10 being the highest stake of 20.00 euro. We then calculated the average change in stake level between two games. Since players overall changed the stakes rather infrequently, the average changes in stake level were quite small. To reduce the number of leading zeros, we therefore multiplied the changes in stake level by 100. The changes in stake level were then analyzed, using the same data analysis methods as in the main text ( Figure S7).

Figure S7
Change in stake levels (*100) after a win and after a loss. Error bars stand for 95% within-subject confidence intervals.
The results were largely in line with those obtained with the changes in stake Table S5 Statistical analyses on change in stake level.  amount (Table S5). There was again a significant main effect of prior outcome, such that players increased the stake level more after a win than after a loss. The only difference was that this effect was statistically reliable in both groups for changes in stake levels, whereas for changes in stake amount, the effect was only statistically reliable in the high-involvement group (see the main text).

Speed of play -raw RTs
In the main text, we used RT z scores as an index for the speed of play, to control for the general difference in the speed of play across players. Here we analyzed the raw RT scores (from starting a game till putting in the first column, in milliseconds) with the same data analysis method.

Speed of play (raw RT values in milliseconds) after a win and after a loss. Error bars stand
for 95% within-subject confidence intervals.
High-involvement players overall played more quickly than low-involvement players ( Figure S8 and Table S6). The main effect of prior outcome was also statistically significant; players played a game more quickly after a loss than after a win, and this effect was observed for both groups of players (see the pairwise comparisons in Table S6).
Furthermore, there was a significant interaction effect between involvement level and prior outcome. To break down this interaction effect, for each player, we calculated a difference score between RT after a loss and RT after a win (i.e., RT dif f = RT loss -RT win ). These difference scores were then compared between the high-involvement and the

Table S6
Statistical analyses on speed of play, using raw RT values (in milliseconds).  low-involvement group. We observed that wins and losses had a smaller influence on the speed of play for high-involvement players than for low-involvement players. However, since the high-involvement players overall played the games much more quickly, this smaller influence of prior outcomes could be (partly) caused by this general difference in the speed of play between the two groups. We therefore reported the analyses with RT z scores in the main text, but included the results on raw RT values here for the sake of completeness.